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In this manuscript, we consider a control system governed by a general ordinary differential equation on a Riemannian manifold, with its endpoints satisfying some inequalities and equalities, and its control constrained to a closed convex…
We study convergence and stability properties of control-affine systems. Our considerations are motivated by the problem of stabilizing a control-affine system by means of output feedback for states in which the output function attains an…
For a general class of dynamical systems (of which the canonical continuous and uniform discrete versions are but special cases), we prove that there is a state feedback gain such that the resulting closed-loop system is uniformly…
Model-based controllers can offer strong guarantees on stability and convergence by relying on physically accurate dynamic models. However, these are rarely available for high-dimensional mechanical systems such as deformable objects or…
Classically, the dynamics in a non-globally hyperbolic spacetime is ill posed. Previously, a prescription was given for defining dynamics in static spacetimes in terms of a second order operator acting on a Hilbert space defined on static…
We consider a broad class of second-order dynamical systems and study the impact of damping as a system parameter on the stability, hyperbolicity, and bifurcation in such systems. We prove a monotonic effect of damping on the hyperbolicity…
In recent years, Neural Networks (NNs) have been employed to control nonlinear systems due to their potential capability in dealing with situations that might be difficult for conventional nonlinear control schemes. However, to the best of…
We consider discrete ensembles of linear, scalar control systems with single-inputs. Assuming that all the individual systems are unstable, we investigate whether there exist linear feedback control laws that can asymptotically stabilize…
Two nested classes of discrete-time linear time-invariant systems, which differ by the set of periodic signals that they leave invariant, are studied. The first class preserves the property of periodic monotonicity (period-wise…
This note proposes a general control approach, called vector-field guided constraint-following control, to solve the dynamics control problem of geometric path-following for a class of uncertain mechanical systems. More specifically, it…
This paper focuses on systems of nonlinear second-order stochastic differential equations with multi-scales. The motivation for our study stems from mathematical physics and statistical mechanics, for examples, Langevin dynamics and…
We are interested in the feedback stabilization of general linear multi-dimensional first order hyperbolic systems in $\mathbb{R}^d$. Using a Lyapunov function with a suited weight function depending on the system under consideration we…
We consider tracking control for uncertain linear systems with known relative degree which are possibly non-minimum phase, i.e., their zero dynamics may have an unstable part. For a given sufficiently smooth reference signal we design a…
We extend the method of controlled Lagrangians with kinetic shaping to those mechanical systems on semidirect product Lie groups with broken symmetry, more specifically to the Euler--Poincar\'e equations with advected parameters. We find a…
In this report we deal with the problem of global output feedback stabilization of a class of $n$-dimensional nonlinear positive systems possessing a one-dimensional unknown, though measured, part. We first propose our main result, an…
In this paper we explore the stabilization of closed invariant sets for passive systems, and present conditions under which a passivity-based feedback asymptotically stabilizes the goal set. Our results rely on novel reduction principles…
Set-based integration methods allow to prove properties of differential systems, which take into account bounded disturbances. The systems (either time-discrete, time-continuous or hybrid) satisfying such properties are said to be "robust".…
We introduce a class of singular partial differential equations, the second-order hyperbolic Fuchsian systems, and we investigate the associated initial value problem when data are imposed on the singularity. First of all, we analyze a…
This paper studies the feedback stabilization of abstract Cauchy problems with unbounded output operators by finite-dimensional controllers. Both necessary conditions and sufficient conditions for feedback stabilizability are presented. The…
Stable concurrent learning and control of dynamical systems is the subject of adaptive control. Despite being an established field with many practical applications and a rich theory, much of the development in adaptive control for nonlinear…